15TH J UNE,
1902.
NOTES ON THE EFFICIENCY OF
LIFTING TACKLE.
By
J A MES S HIRRA .
In the cons tru ction and repair of heavy machinery,
s uch as marine engines, we a re constantly obliged t o
use lifting appli ances t o carry ou t the work. The same,
of course, could be said of all cons tru ctive work-bu t
he did n o t propose here to trea t either of the hodman
who carried the bricks and mortar of a tall building on
his shoufders up a series of inclines , nor of the fixed
s team derrick whi ch now so often did the work-but t o
confine his attention to such hand tackle as would be
used in and about a work shop , or be s upplied a s part of
the outfIt accomp anying a s teamship's m achinery, su ch
as screw-ja cks , block s and tackle , etc . And by efficien cy, he meant ' principally mechanical effi ciency, or
the proportion of useful work actually done by the
machine t o th at exerted on it, though strength and
handiness migh t also be referr ed to . Every one who has
'ha d t o lift heavy weights jn a limited space and wit h 3.
limited s taff of labour m ust often have observed that the
output of s uch machines is very disappointing, even
when in g ood cond ition , and that when they are in what
is too often their condition, dirty, r usty, and either free
from lub rication, or with the oil on them everywhere bu t
where it is wanted, t o call them effi cient a t all is really
t o t a ke a liberty with lang uage . In shops where the
tackle s, screw-jack s , etc. , a re in cons tant use, the economy of keeping them in good working condition is soon
EFFIC m NC Y OF LIFTIN G TACKLE .
49
b r ought home t o the. ma nagement, but wHere 1 he heavier
tackles are only used at rare inter vals, and out of sight
and mind most of the time , as in a steamer's engin eroom, they are often found wanting in some respects
when needed, and though the work may be carried
through in the long run, a quite unnecessary and incom'mensurate amoun t of en ergy, physical and spiritual, is
expended and dissipated in to hea t in the operation.
As regar d s the theoretical mechanical advantage or
"purchase" gained by lifting tackles, t'his is usuaHy
ea sily calc ulated from the velocity ratio of the re ceiv.in g
and delive ring parts of the machine, the part whe re
energy is impressed upon it, and tha t where it is
e xpended upon the work t o be done , but t he k nowledge
s o gained is only half knowledge without knowin g the
-practical hindrances that dis count it. He fo und, however, that even t'his theoretical advantage is a mystery
to many engineers, who, no doub t , know well enough
the p ractical use of s uch tackle s , a n d that the study of
applied ' me chanics, the very r udiments of a n engineer's
educ a tio n, is too oft en neglec ted by those, for inst a nce,
wh o proposed to take ou t certificates of compe tency a s
marine engineers . It wa s this observation that led hIm
t o revise hi s own studies on the subject, and t o bring
it before this Associ ation in the hope of ge t ting some
us eful h int s for his own benefit, and to show tha t the
unknown q uan tities which we so easily negle ct on paper,
are of supreme impor tanc e- the kn owledge of e1ement°ary theory mu st be supplemen t ed by p ractical experim,ent if it is to be of any use t o us . The simples t lifting
machine s , if we may call them so, are the lever and the
wedge. T he lever, in its simplest form, that of the pinch
or crow-bar, 'ha s the unique advantage of bein g almos t
fri ctionle ss , its moti on on its f ulcrum being usually a
rolling one , and when thi s fulcrum or 'heel a nd the ba r
itse]f were rigid, and the bar balanced, all the work put
in at one end of the arra n g ement is returned at the
other , in other words , its efficien cy is 100 p er cent. But
this very rolling, unless on a knife edge a s in a weigb ing machin e , introdu ce s a complication in the calculation
of the mechanical advan tage or purchase gaine d . Take ,
for ins tan ce, an ordinary crowba r Jittmg a weigh t- here
50
E FFICIENCY OF LIFTING TACKLE .
t he purchase was the ratio of the weight "lifted to the
verti cal effort on the long arm of the lever, and is
inversely proportional to the horizontal projections of the
a rms-but as soon as movement takes place, owing to
change of position of the fulcrum by the curved knee of
the bar rolling on its support, the ratio was altered,
though the efficiency remained the same, and to calculate the rate a t which the purchase varied would require
considerable mathematical skill. He mentioned this to
show what food for thought we have even in the simplest
m echanism . Another matter for thought is, why do we
gain any effe ct by using a lever?
We usually say,
"Because of the leverage," like the texicographer's famous definition of an archdeacon-a Clergyman who exercises archdeaconal fun ctions-involving the expression
without in any way enlightening us. It is because of the
g rea t fundamental principle of all machinery that .t he
energy developed, or work done, is exactly equal to that
introduced or impressed upon the machine, and if none is
lost in internal work or fri ction, we retained the
same output as we put in. It is diffi cult to convince "the
man in the s treet," he did not say the engineer, of
course, that mechanical work, that is the energy which
is measured by the produ ct of pressure and motion, was
a real entity, and not a mere convention; while pressure
a nd motion by themselves were b ut mere ideas , of no
objective reality until they are combined. The pressure
in a boiler under hydraulic test may seem a very real
thing-but it does not produce a m otion in the molecules
of the m etal-if the s tres s does not produce a strain,
it was a mere phil osophical motion. The term "pressure"
is certainly a useful one , and one we could ill afford to
do without, but it can only be defined as a "tendency,"
and is only apparent to us throu gh the motions it produce s . But the product of th e s tre ss and the strain is
work. and this is what t ries the boiler under test. To the
practical man this might seem a mere philosophical
notion itself, but the so-called practical man has often a
lot to learn, he found. " Well, then, if a loaded lever like
a' scale-beam or a steel yard is , in equilibrium, it is because the same amount of work would have to be expended in raising either end of t he system, and there
lill<:FI I E ' OY 0 .'" LIFT ING 'l'AOKLE.
being nothing to determine the bar to move either way,
it necessarily stands still. As we say, the '.momenl"
round the fulcrum of either weight is the same, but this
·word "moment" is just a convenient expression th a t
explains nothing. To move the bar some external work
must be done on it and set it oscillating; and then, t oo,
at any instant, the kinetic energy a ccumulated in the
moving weights is equal to the work so impressed; less
that" expended in friction at the points of suspension and
in agitating 'the surrounding air, which gradual~y converts the en ergy of work into that of heat , and brings
the bar t o rest again. The same thing holds for all
machines- -the sum of the external or useful work done ,
and that done intern ally, as in overcoming friction, or
being stored up in spring s, or accumulated in moving
masses, must equal the work put into it. When a lever
is hung- in bearings, like the pump levers of an engine,
the effect of sliding fri ction occurs at once , and the
efficiency is necessariIy less than when rocking on a
knife edge or rollin g on
curved surface . The work so
'lost is proportional to t he radius of the gudgeon , and t o
the sum of the pressu re s on t he ends of the lever and
also that due to its own weight . COQsequently, if this
sum be a large one , though the effor t neede d t o balance
t he weight may be very small, the friction may be very
considerable, and the efficiency much impa ired.
T his:
fact, that the friction is usu ally a fu nction , not of the
effort only, but of the effort and resis tan ce combined,.
IS what makes the necessary effort in practice so much.
g reater than what t heory leads us t o expect , the tact
being, of course, that we use an incomplete theory, and
one that neglects indispensible f acts .
Another appa rently simple appliance fo r lifting
weights or applying energy , is the wedge , but m Its
primitive fo rm it is used in conjunction with the hammer
0r maul, and the combin ation leads us at once into quite
another field, wherf percu ssive a ction , elas ticity, and
dynamic forces th a t alm ost defy calculation, come in to
a ction . The wedge, a ctuated by simple p ressure, is useful sometimes, as for p rodu cing an easily gra duated
motion of sligh t extent, but the linear motion of a nne
wedge being so g reat in proportion t o its useful compon--
a
52
EFFICIEN CY OF LIFTI NG TACKLE .
ent, and the frictional resistance bearing a definite ratio,
usually a large one, t o the wh ole weight lifted, and actmg over the whole travel of the wedge, it may, and
often does, form n early the wh ole of the resistance to
mot~on, and leaves the efficiency low indeed. Suppose,
for mstance, we try to lift a weight by a dead pressure
on a wooden edge inserted between two surfaces of
wood. The co-efficien t of friction may be a s much as
· 5, corresponding to an "angle or repose" of 30 deg. ,
and both sides of the wedge encounter this resis tan ce ,
making it equal t o unity, so that simply to move the
wedge req uires greater effort than t o lift the weig ht
through an equivalent dis tan ce directly. The >useful
work is that due to the t aper of the wedge, but a vast
amount of dea d work has to be done before it takes
e ffec t. If the taper be I in 1 0, the work nece ssary t o
lift W lbs. I foot, is practically, with the above amoun t
of friction, 10 W + W
11 W foot-Ibs, 1'10 that t¥-
=
of
the whole
only
1\ th or
work
9%.
is
lost, and the efficiency is
This
is
sometimes expressed
by saying "Co unter-effi ciency" is I I, i.e ., I I times the
useful work mu s t be expended in the operation. The
e ffort required, or pressure on the end of the wedge,
instead
of
being
-frJ
W,
is now
1
-r.,j, and there is
no mechanical advantage whatever . In p ractice, where
the wedge would be dri ven with a hammer, its elasticity
and compression and the ensuing vibration, would lessenthe frictional re sis tance indefinitely, and the effort driving it would be accumulated work in the hammer head,
which is a dillerent thing from a dead pressure . The
hammer mu sf remain in contact with die wedge for some
definite time after impact, during which it is, as we say,
giving up its momentum to it, but the total work done
by the wedge, useful and frictional, mu st equal that
s t ored in the hammer in its descent. It is a common
error to reck on the force of a blow a s a pressure, and to
confound kinetic energy and weight-if a body fallsif a poor fellow jumps fro m the top of a burning building
15 0 feet highthe "ma n in the street" s tarts inquiring
how much his weight was multiplied by the fall, and
some scientis ts profess t o give him an answer. The
m omentum which is a mere rna thematical ratio, of no
EFFICI ENCY OF LH'TING 'f ACKL E .
53
objective mea ning, is what they mean , but the accumula ted work, due to the distan ce fall en is the real fa c tor
in the case . The wedge , by itself , then, is n ot ot much
consequence as a lifting ma chine, but is only a convenien t mode of app lying the outp ut of some other mechan ism or s tore of energy through . We coil our wedge or
inclined s urfa ce on a mandril, and ma ke a screw of it,
turning in a nut, but s till the screw without a lever would
be a poor a ffair , so we apply a "tommy" bar t o the head
of the s crew to give the effort a grea ter radius of action ,
an d have the screw-jack. The theoretical advantage or
pO'wer gained, as we say, by this machine, can be calculated from the ra tio of the pitch of screw to the circumferen ce desc ribed by the end of t he lever, but the
efficiency depe nds on the fri ct ional resistance ; and
is seldom more than 25 per cent.- t hat is, the actual
pressure on the lever is abou t 4 t imes or more than that
which is theoretically n ecessary; and the r ubbin g s urfa ces may even seize an d se t fa st, when the efflc ienr.y
would of course be nil.
To measure this frictional
resistance and elab orate a form ula for it, a comprehensive series of careful experiments would be n ecessarybu t assu ming that the ordinary laws of friction are
applicable, let us see what we can do with the data at
h and. Le t us t ake a screw of 1 in. pitch, square thread,
outs·i de diame ter 21 inch and I t inch at bo t tom of
thread, so that it s mean ra dius is I inch, worked by a
lever 20 in . long, and carrying a weight of 2,000 lb s . on
cap with an a nnu lar hearing on t op of screw of 4
square inches area, and also a mean radius of I in.,
which would correspond t o outside a nd inside diameter
of a bout 2t
in. a nd
l ~.
in.
'l' be we ight p .. odllees a
frictional resistance both at the threa d and a t the cap
bearing . T he intensity of p ressure at the cap will be
2000/4 , eq ua l to 5 00 lbs. per sq. inch, which is not too
high at sl ow speeds t o altoget her squeeze out a lubricant
of good body, s o we may t a ke the co-efficien t of friction
as
for
110-- lian ki ue Ii. uotes
Rmooth
surfaces
.08 0 1'
lnhricated .
lz
We
as
tbe
Rhall
co efficient
take t.he
co-efficien t at t he thread to be the same , the bearing
area is usually much greater here than at the cap, owing
.t o the pre s sure heing spread over several convolutions of
54
EFFICIENCY OF LIFTING 'PACKLE
the thread a t once, and the lubrication should be a t least
as good. The fri ctional resis tan ce at the cap will then
b e 2000/lO = 200 (bs., and it acts throug h 1\ space
2 1' 1 incheR, or 6.2832 inches
.5236 foot.
t he foot Ibs. work Jost hers in one revolution will
200 x .5236 = 104 72.
A t th e thread t.here is
of
So
be
a
g reater pressure than a t the cap owing to its carrying
th.e weigh t of the screw also, but we may neglect that
a t present . There is, 'however, a g reater normal pressure bet ween the surfaces than that due to the direct
weight, because there is also a turning effort or tenden cy
to run down , which fri ction resist s , and the normal pressu re is the res ult ant of that and of the weight. Thic:;
normal pressure bears t he same proportion t o the weigh t
as t he length of one turn of the threa d does to its projected circle's circumference . With a fine t hread t he
difference is not mu ch- in t his ca se the two lengths are
6.303 inches and 6 .28 32 in ches, and the pressure on the
th read
is
this, or
and
the
revolu tion
6 303 = 2006 l bs.
Th en itr of
6.2882
2006 lbs. IS the frictio nal r esistance her e,
di stance i t is overcome through 1D one
heing 6303 '! or
525 foot..
th e product.
2000
X
10 5. 3 foot lbs . is the work absorbed at the thread, if
we suppose t he effort applied parallel to the surfaces in
con tact, but a s it is applied perpendicular to the axi s
and at a n angle with these surfaces, some of the effort
goes, to increase the normal pressure between t hem still
further. We m ay arrive at the t rue amount by g raphic
construction or trigonometrical calculation, bu t with fine
pit ched screws the slight excess may be neglected
Hen ce the combined frictional loss a t t hread and cap is
105.3
+
104.7
or
210 foot
(bs. per r e vol ution .
The
useful work is 2000 lbs. lifted ! " equal to 83 .3 foot lbs. ,
and the t otal work impressed on lever in one revolution
is therefore 293 ft. Ibs. T he circumference of circle
described by end of lever being 10.47 feet, we would
need an effort of 293 10-47, equal to 2 8 lbs. , to move the
weight, which 83.3 10.47, equal a little under 8 lbs.,
would have done had there been no friction, and the
efficiency is
83.3 X 100
= about 28 per cent.
293.3
EFb'ICIENCY
0];'
55
LI FTING TACKLE .
The co-efficient of friction is the tangent of the angle
<Jf tepose of the surfaces, or that angle with the horizon
.at which sliding would begin under the ihfluence of
gravity onl y . To get the true effort to overcome the
friction of the thread and lif t the weight, we take it a'5
proportional to the tangent of the sum of the two angles
- the pitch angle or that made by the thread with a line
perpendicular t o the axi s-and the angle of repose. In
the above case the pitch angle is 4 deg. 33 min. , for t he
tangement
of
that
angle
is 6 ' 85
.~ ;j~
pitch divided by
-circumfe r ence = .07958, while the ang le of re pose is that
WhORO tangement is .1, Rnn
1"
5 neg. 42
mm.,
the sum of these a ngle s is 10 deg . IS min., whose tan'g ent is .1 808 3, only slig htly in excess of the s um of the
tangents themselve s at the se small angJes. This number, then, is the ratio of effort to ' weight if applied at
ra dius of screw thread) or I inch, and if applied wi th a
lever 20in. long, it will be proportionately redu <;:ed to
l. 8083/ 20
.009.
With
a
load
of
~!OOO
Ihi!,
this
gives us 181bs. as effort needed . The cap resistan ce
being calculated and added a s before brings up the eff or t
t o 281bs.
The efficiency of the screw-j a ck, neglecting for the
present the cap friction, that is, supposing the weight
to revolve with t he screw, as when one sits on a screwup mu sic s tool a nd spins it round and up, is, if we call
the angle of pitch m, and that of repose n, equ al to
t,an m .
tan. (m X n )
.equal in the above case to
.07958
.18083
= 44
per cent.; with fine pitches and g ood lubrication thi'5
{}oes
not
differ
m aterially
from
tan. m
but
tan. (m + D)
with
'coarse pitch or mu ch friction it would greatly fall short
·of it . For instance, if the pitch angle was 45deg ., t hat
is, if the pitch was equal to 3.141 6 times the diameter,
and the
co-efficient
was
frJ
as before,
th e
sum of t he
tangents would be I . I, but the tang ent of the sum,
50deg. 42min., would be 1. 222, and the efficiency would
,56
not b.e
EFFICIENCY OF' LIF'.rI NG TACK LJ<j.
1
or 90 pe l' ce nt, but
1
or 82 pel' cent.
[i
1.22~
Here we see the effi ciency is mu ch greater than with
the fine p itch , but there is no mechanical advantage
gained by the scre w it self, thoug h there would be some
"purchase" from t he lever used to turn it . Screws of
this long pitch a re n ot, of course, used in screw-j acks,
but occasionally a re in mechanism, the common t wist
brace fo r drilling small holes being an instance . Th us
we see nearly three-fourths of the effort and work done.
IS lost in a fairly lubricated, not over-loaded jack ; how
much more m ust be when the oil. is a bs<;nt, a nd t he pres,
sure poss ibly concen trated on one edge of the thread
or cap, m aking it seize and abrade, instea d of sliding !
If the t hread is triang ul ar in section the friction is m uch
increased, the normal pressure between the surfaces
being increased as the slant side of the thread section
is to the dept h of it . In t he Whitworth t hread the slant
is about Ig the depth, so the friction is in creased a bout
I3 per cen t. over wha t a square threa d would give, and
t he efficiency correspondingly lowered.
T he g reat er
s trength of the section is some compensation fo r this,
but the "buttress" threa d as fo rmerly used in t he breech
blocks of big guns would be as strong as the ordinary
shape, and have no more friction than the sq uare thread ;
of course , it could be used for screws that overcome
resistance in one direction only . I say "formerly used, '"
fo r I notice modern breech-loaders h ave the ordina ry
isoseeles t riangular thread. Whit worth' s early breech
blocks had not only a buttress thread, but the fa ce of
It was undercut, so tha t it tended to bind the breech
together under the p ressure of firing instead of to burst
it, a s with the ordinary form, bu t t his has been g iven up,
owing, I presume, to its g reater lia bility to jamb. The
great loss of efficiency by fri ction is not without some
compen sation--it effect ually preven t s the weight overhauling t he screw or running down of itself. If t he
efficiency is m ore than 50 per cent . this may occur, a ne!some constant pressure on the t urning bar be necessary
to prevent it, when the weight was not being lifted . So·
it gives us a very efficient brake , bu t a t an unreasonable
expense. The efficiency is about the maxim um when